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Q.

Four thin rods each of mass m and length / are joined to make a square. Find moment of inertia of all the four rods about any side of the square.

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a

(1) $\frac{1}{3} {ml}^{2}$

b

(2) $\frac{5}{3} {ml}^{2}$

c

(3) $\frac{7}{3} {ml}^{2}$

d

(4) $\frac{1}{2} {ml}^{2}$

answer is B.

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Detailed Solution

$I = I_{1} + I_{2} + I_{3} + I_{4}$

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$= 0 + \frac{{ml}^{2}}{3} + {ml}^{2} + \frac{{ml}^{2}}{3} = \frac{5}{3} {ml}^{2}$

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Four thin rods each of mass m and length / are joined to make a square. Find moment of inertia of all the four rods about any side of the square.